一类变系数线性系统的稳定性

<正> 变系数动力系统运动稳定性是现代化生产中急待解决的一个课题,我国有不少学者正从事于这一课题的研究〔1—4〕,美国Lefschetz动力研究中心仍然把变系数线性系统的运动稳定性作为重要的研究项目之一。文〔3〕利用分解理论研究了缓变系统与子系统呈对称型的大系统的稳定性。本文放宽了对子系统为对称及缓变的要求,沿用分解理论研究了一类仿拟反对称系统平凡解的稳定性。

THE STABILITY OF A TYPE OF LINEAR SYSTEM WITH VARIABLE COEFFICINTS

We consider the linear time-Varying systemwhere × denotes an n-dimensional vector arid A(t) is an n × n matrix,The elements ai(t) (i = 1, 2,……, n) are continuous and bounded for t≥t.and suppose that A1(t), A2(t), ……Ar(t) are respectively n1×n1, n2×n2,……, nr×nt parareflexive quasi-symmetric matrixes (n1+n2+……+nr =n) .Theorem.If every Ai(t) (i=1, 2,……r) are respectively ni×ni pararefle- xive quass-symmetric matrixes in systems (1) .For every Ai(t), we haveThe elements aij(t) (i, j= 1, 2 ……n) are continuous and bounded for t≥toThe elements of the interconction term are bounded, i.e.and all roots of the equationhave negative real part, wherethen the trivial solution of system ( 1 ) is asymptotically stable.Because the ystem of linear, then stable is global.